A note on the numerical solution of singular integral equations of Cauchy type
This manuscript presents a method for the numerical solution of the Cauchy type singular integral equations of the first kind, over a finite segment which is bounded at the end points of the finite segment. The Chebyshev polynomials of the second kind with the corresponding weight function have been...
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| Format: | Article |
| Language: | English |
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World Academy of Science, Engineering and Technology
2009
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| Online Access: | http://psasir.upm.edu.my/id/eprint/12767/ http://psasir.upm.edu.my/id/eprint/12767/1/A%20note%20on%20the%20numerical%20solution%20of%20singular%20integral%20equations%20of%20Cauchy%20type.pdf |
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| author | Mahiub, Mohammad Abdulkawi Eshkuratov, Zainidin K. Nik Long, Nik Mohd Asri |
| author_facet | Mahiub, Mohammad Abdulkawi Eshkuratov, Zainidin K. Nik Long, Nik Mohd Asri |
| author_sort | Mahiub, Mohammad Abdulkawi |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | This manuscript presents a method for the numerical solution of the Cauchy type singular integral equations of the first kind, over a finite segment which is bounded at the end points of the finite segment. The Chebyshev polynomials of the second kind with the corresponding weight function have been used to approximate the density function. The force function is approximated by using the Chebyshev polynomials of the first kind. It is shown that the numerical solution of characteristic singular integral equation is identical with the exact solution, when the force function is a cubic function. Moreover, it also shown that this numerical method gives exact solution for other singular integral equations with degenerate kernels. |
| first_indexed | 2025-11-15T07:50:59Z |
| format | Article |
| id | upm-12767 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T07:50:59Z |
| publishDate | 2009 |
| publisher | World Academy of Science, Engineering and Technology |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-127672019-10-31T04:16:56Z http://psasir.upm.edu.my/id/eprint/12767/ A note on the numerical solution of singular integral equations of Cauchy type Mahiub, Mohammad Abdulkawi Eshkuratov, Zainidin K. Nik Long, Nik Mohd Asri This manuscript presents a method for the numerical solution of the Cauchy type singular integral equations of the first kind, over a finite segment which is bounded at the end points of the finite segment. The Chebyshev polynomials of the second kind with the corresponding weight function have been used to approximate the density function. The force function is approximated by using the Chebyshev polynomials of the first kind. It is shown that the numerical solution of characteristic singular integral equation is identical with the exact solution, when the force function is a cubic function. Moreover, it also shown that this numerical method gives exact solution for other singular integral equations with degenerate kernels. World Academy of Science, Engineering and Technology 2009 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/12767/1/A%20note%20on%20the%20numerical%20solution%20of%20singular%20integral%20equations%20of%20Cauchy%20type.pdf Mahiub, Mohammad Abdulkawi and Eshkuratov, Zainidin K. and Nik Long, Nik Mohd Asri (2009) A note on the numerical solution of singular integral equations of Cauchy type. International Journal of Applied Mathematics and Computer Sciences, 5 (2). pp. 90-93. ISSN 1307-6906 |
| spellingShingle | Mahiub, Mohammad Abdulkawi Eshkuratov, Zainidin K. Nik Long, Nik Mohd Asri A note on the numerical solution of singular integral equations of Cauchy type |
| title | A note on the numerical solution of singular integral equations of Cauchy type |
| title_full | A note on the numerical solution of singular integral equations of Cauchy type |
| title_fullStr | A note on the numerical solution of singular integral equations of Cauchy type |
| title_full_unstemmed | A note on the numerical solution of singular integral equations of Cauchy type |
| title_short | A note on the numerical solution of singular integral equations of Cauchy type |
| title_sort | note on the numerical solution of singular integral equations of cauchy type |
| url | http://psasir.upm.edu.my/id/eprint/12767/ http://psasir.upm.edu.my/id/eprint/12767/1/A%20note%20on%20the%20numerical%20solution%20of%20singular%20integral%20equations%20of%20Cauchy%20type.pdf |